College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Title: Determining the Direction of Vector**
**Question:**
The direction of the vector **A** = 4i + 4j is
**Options:**
* 0°
* 45°
* 90°
* None of these
**Explanation:**
To determine the direction of vector **A** represented as 4i + 4j, we use the concept of vector direction calculation. The vector components are along the x-axis (i) and y-axis (j).
The formula to determine the direction (θ) of a vector (A = ai + bj) with components a and b is:
\[ θ = \tan^{-1} \left(\frac{b}{a}\right) \]
Substituting the given values (a = 4, b = 4):
\[ θ = \tan^{-1} \left(\frac{4}{4}\right) \]
\[ θ = \tan^{-1}(1) \]
This results in:
\[ θ = 45° \]
Therefore, the correct answer is 45°.
**Answer:**
* 45°](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2291e09-7fcf-4fac-bc31-e34a7ce4842f%2F8fad4a42-b3c1-4d6c-b58d-4ae9ebbe0b60%2F0d0jvff_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Determining the Direction of Vector**
**Question:**
The direction of the vector **A** = 4i + 4j is
**Options:**
* 0°
* 45°
* 90°
* None of these
**Explanation:**
To determine the direction of vector **A** represented as 4i + 4j, we use the concept of vector direction calculation. The vector components are along the x-axis (i) and y-axis (j).
The formula to determine the direction (θ) of a vector (A = ai + bj) with components a and b is:
\[ θ = \tan^{-1} \left(\frac{b}{a}\right) \]
Substituting the given values (a = 4, b = 4):
\[ θ = \tan^{-1} \left(\frac{4}{4}\right) \]
\[ θ = \tan^{-1}(1) \]
This results in:
\[ θ = 45° \]
Therefore, the correct answer is 45°.
**Answer:**
* 45°
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